document.write( "Question 824808: if carter peak height at the basket of leaped for a dunk and reached a 1.07m, what was his upward velocity in meters per second at the monent his feet left the floor: and find the amount of time he was in the air?
\n" ); document.write( "v1^2=v^20 +2gS
\n" ); document.write( "S=1/2 gt^2+v0t \n" ); document.write( "

Algebra.Com's Answer #496869 by KMST(5328) $\"\"$ $\"About$

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IF THIS IS PHYSICS:
\n" ); document.write( "Since movement is along a straight line, we can indicate direction (upwards or downwards) by assigning a positive sign to measures of displacement, velocity, and acceleration in one direction. Displacement, velocity, and acceleration in the opposite direction are assigned a negative sign. It does not matter which direction is taken as the positive direction, as long as you do not forget halfway through the problem.
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\n" ); document.write( "I say upwards is the positive direction.
\n" ); document.write( "I say position 0 is the start of the leap,
\n" ); document.write( "and position 1 is at the top of the leap.
\n" ); document.write( " $\"S=1.07m\"$ is the positive displacement of the leaper (distance from floor to feet) at the highest point of the leap, position 1.
\n" ); document.write( " $\"t\"$ is the time rising to the top of the leap,
\n" ); document.write( " $\"g=-9.8\"$ $\"%22m%2F%22+s%5E2\"$ is the acceleration (negative because it is downwards),
\n" ); document.write( " $\"v%5B0%5D%3E0\"$ is the velocity at the start of the leap, position 0.
\n" ); document.write( " $\"v%5B1%5D=0\"$ is the velocity at the top of the leap, position 1.
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\n" ); document.write( "IF THIS IS JUST MATH:
\n" ); document.write( "You've been given two magical formulas:
\n" ); document.write( " $\"v%5B1%5D%5E2=v%5B0%5D%5E2%2B2gS\"$ and $\"S=v%5B0%5Dt%2B%281%2F2%29gt%5E2\"$ .
\n" ); document.write( "Since you do not know $\"t\"$ , you'll have to use $\"v%5B1%5D%5E2=v%5B0%5D%5E2%2B2gS\"$
\n" ); document.write( "Substituting the values listed above, with meters and seconds in the units,
\n" ); document.write( " $\"0%5E2=v%5B0%5D%5E2%2B2%28-9.8%29%2A1.07\"$
\n" ); document.write( " $\"0=v%5B0%5D%5E2-20.972\"$
\n" ); document.write( " $\"v%5B0%5D%5E2=20.972\"$
\n" ); document.write( " $\"v%5B0%5D=sqrt%2820.972%29\"$
\n" ); document.write( " $\"highlight%28v%5B0%5D=4.6%29\"$ $\"%22m%2Fs%22\"$
\n" ); document.write( "
\n" ); document.write( "IF THIS IS PHYSICS:
\n" ); document.write( " $\"v%5B1%5D=v%5B0%5D%2Bgt\"$ and $\"S=v%5B0%5Dt%2B%281%2F2%29gt%5E2\"$
\n" ); document.write( "do not seem useful by themselves
\n" ); document.write( " $\"%28v%5B1%5D%2Bv%5B0%5D%29%2F2\"$ is the average velocity, so $\"S=%28v%5B1%5D%2Bv%5B0%5D%29t%2F2\"$ .
\n" ); document.write( "From there we can get to $\"S=v%5B0%5Dt%2B%281%2F2%29gt%5E2\"$ , but we can also get to $\"v%5B1%5D%5E2=v%5B0%5D%5E2%2B2gS\"$ .
\n" ); document.write( " $\"S=%28v%5B1%5D%2Bv%5B0%5D%29t%2F2\"$ --> $\"2S=%28v%5B1%5D%2Bv%5B0%5D%29t\"$ --> $\"t=2S%2F%28v%5B1%5D%2Bv%5B0%5D%29\"$
\n" ); document.write( "Substituting $\"2S%2F%28v%5B1%5D%2Bv%5B0%5D%29\"$ for $\"t\"$ into $\"v%5B1%5D=v%5B0%5D%2Bgt\"$ we get
\n" ); document.write( " $\"v%5B1%5D=v%5B0%5D%2B2gS%2F%28v%5B1%5D%2Bv%5B0%5D%29\"$
\n" ); document.write( " $\"v%5B1%5D-v%5B0%5D=2gS%2F%28v%5B1%5D%2Bv%5B0%5D%29\"$
\n" ); document.write( " $\"%28v%5B1%5D-v%5B0%5D%29%28v%5B1%5D%2Bv%5B0%5D%29=2gS\"$
\n" ); document.write( " $\"v%5B1%5D%5E2-v%5B0%5D%5E2=2gS\"$
\n" ); document.write( " $\"v%5B1%5D%5E2=v%5B0%5D%5E2%2B2gS\"$ \n" ); document.write( "

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